Is it statistically significant? The chi-square test

UAS Conference Series 2013/14

Is it statistically significant? The chi-square test

Dr Gosia Turner Student Data Management and Analysis

4 February 2014

14 September 2010

Page 1

Why chi-square?

? Tests whether two categorical variables are independent (no relationship)

? sex and proportion of First ? divisions and degree classification ? ethnicity and proportion of Firsts ? Categorical variables: sex, school type, ethnicity, classified exam result (1st, 2.1, 2.2, 3) but not age, average exam mark

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Observed vs. expected

? There are 4,000 finalists ? The probability of getting First is 50% ? 2,000 males and 2,000 females ? How many males and how many females would you

expect to get First? ? 1,000 males and 1,000 females (50% of 2,000) ? But the observed values are 1,200 and 800 ? Is it significant?

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Steps to follow

? State the hypothesis ? Calculate the expected values ? Use the observed and expected values to calculate the

chi-square test statistic ? Establish the significance level you need (usually 95%

p = 0.05) and the number of degrees of freedom ? Compare the chi-square statistic with the critical value

from the table ? Make a decision about your hypothesis

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Hypothesis

Hypothesis Observed values Expected values Calculation of chi-square Degrees of freedom Compare with the table

Conclusion

? H0: There is no association between gender and proportion of Firsts (the proportion is the same for males and females)

? H1: There is an association between gender and proportion of Firsts (the proportion is

different for males and females)

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